Cancer is a dynamic disease. During the course of disease, cancers generally become more heterogeneous. As a result of this heterogeneity, the bulk tumour might include a diverse collection of cells harbouring distinct molecular signatures with differential levels of sensitivity to treatment. This heterogeneity might result in a non-uniform distribution of genetically distinct tumour-cell subpopulations across and within disease sites (spatial heterogeneity) or temporal variations in the molecular makeup of cancer cells (temporal heterogeneity). Heterogeneity provides the fuel for resistance; therefore, an accurate assessment of tumour heterogeneity is essential for the development of effective therapies. Multiregion sequencing, single-cell sequencing, analysis of autopsy samples, and longitudinal analysis of liquid biopsy samples are all emerging technologies with considerable potential to dissect the complex clonal architecture of cancers. In this Review, we discuss the driving forces behind intratumoural heterogeneity and the current approaches used to combat this heterogeneity and its consequences. We also explore how clinical assessments of tumour heterogeneity might facilitate the development of more-effective personalized therapies.